Why does the top displace modifier always switch to the active texture?
When selecting the texture to edit, you are actually setting the texture to be used by the displace modifier(s) and anything else that was using the texture that was there before you set it.

It's the same with materials:

Say I want to edit the blue material. If I select the blue material with the orange object selected, I'll turn the orange object blue:



Instead, I should select the blue object:



I have to select the blue object.

To "select" a texture being used by a displace modifier, either click the button next to the texture slot in the modifier:



Or in the texture panel, select which modifier you want to edit, instead of which texture:





If you want to be able to edit a specific datablock regardless of the object selection, you can Pin a panel by clicking the pin:



This will prevent that panel from displaying another object's datablocks until it is unlocked again.